The use of flexible couplings for interconnecting driving and driven shafts of precision instruments wherein the coupling is capable of accommodating shaft misalignments and axial shaft movements and permits limited torsional or radial deflection thereof is well known. Some examples of such flexible couplings are shown by U.S. Pat. No. 4,203,305 which discloses a flexible coupling for torque transmission having a plurality of helical beams, and by U.S. Pat. No. 3,071,942 which discloses a flexible coupling having a first plurality of parallel slots cut into a body and a second plurality of parallel slots cut between the first plurality at a 90.degree. angle. In both examples, a portion of the ends of two shafts are inserted into the bores of hubs at opposite ends of the coupling. Each hub has a bore which has an inside diameter essentially the same as the diameter of the shaft which is to be inserted therein. After insertion, the shafts are fixedly attached to the hub by a set screw threaded into an aperture in the side of the hub. Unfortunately, the use of a set screw forces the shaft, within the tolerance of the bore of the hub, to move to a side of the bore opposite that of the set screw. Because the shaft is not aligned in the bore of the hub, dynamic loading of the flexible coupling results and thereby reduces the effectiveness of the flexible coupling's ability to transfer torque smoothly from the driving shaft to the driven shaft. Sometimes a shaft is fixedly attached to a hub by a separate single or double slotted clamp or, in some cases the shaft is fixedly attached to a flexible coupling body by a hub-slotted clamp assembly which is integral to the body as shown in U.S. Pat. No. 3,150,506. Whether an integral or separate, single or double slotted clamp is used to secure the shaft, such devices often cause the shaft, within the tolerance of the bore, to move to the side opposite that of the clamping screw. This in turn causes static and dynamic imbalance and dynamic loading of the flexible coupling, which reduces its effectiveness for transferring torque. The flexible coupling of the present invention incorporates an improved clamping mechanism to effectively reduce the static and dynamic imbalances caused by the clamping systems of the prior art, thereby eliminating the imbalances and preloading of the coupling.